How light modifies the electron–electron interaction under extreme conditions

•A time-dependent electromagnetic field can modify the electronic interaction.•Analytical expressions of this three-body light matter interactions are presented.•Effects can be evaluated with the amplitude of the laser and electronic distance.

In the domain of extreme light–matter interactions, we show that the electron–electron interaction can be modified coherently by the electric field of the light. The latter play the role of a third partner not only acting on the electrons individually but also on their mutual interaction. By using an original formalism based on the Foldy–Wouthuysen transformation and applied to the Dirac–Breit Hamiltonian in the presence of a time-dependent electromagnetic field, we obtain analytical expressions of new three-body light–matter interactions.